Modal reduction principles across relational semantics

The present paper establishes systematic connections among the first -order correspondents of Sahlqvist modal reduction principles in various relational semantic settings, including crisp and many -valued Kripke frames, and crisp and many -valued polarity -based frames (aka enriched formal contexts). Building on unified correspondence theory, we aim at introducing a theoretical environment which makes it possible to: (a) compare and inter -relate the various frame correspondents (in different relational settings) of any given Sahlqvist modal reduction principle; (b) recognize when first -order sentences in the frame -correspondence languages of different types of relational structures encode the same "modal content"; (c) meaningfully transfer and represent well known relational properties such as reflexivity, transitivity, symmetry, seriality, confluence, density, across different semantic contexts. These results can be understood as a first step in a research program aimed at making correspondence theory not just (methodologically) unified, but also (effectively) parametric.